Shim was found dead on the side of a road at daybreak, 10km west of Ghazni city.
He was in Western clothing and wearing glasses.
Qari Mohammad Yousuf Ahmadi, a Taliban spokesman, told Reuters by telephone on Monday: “We shot dead a male captive because the government did not listen to our demands.”
The South Koreans were abducted on July 19 while travelling on the highway between Kabul and Kandahar, about 140km south of the Afghan capital.
Al Jazeera’s Bernard Smith said that the Afghan president’s office had held a news conference on Tuesday saying it did not want to turn hostage-taking “into an industry”, having been criticised over previous deals with the Taliban.
“The government seems to have drawn a line,” Smith said.
He also reported a military build-up which could be linked to the hostage standoff and that there had been a rise in the number of attacks on the Kabul-Kandahar highway.
Earlier, Al Jazeera received an exclusive video showing some of the female South Korean hostages wearing headscarves, with fighters in the background.
Its authenticity as well as when and where it was made could not be verified.
The South Korean embassy in Afghanistan has refused to comment on the case.
The leader of the group, Bae Hyung-kyu, a 42-year-old pastor, was shot dead on Wednesday and his bullet-riddled body found in a desert area of the province.
Bae’s body arrived in South Korea on Monday.
Al Jazeera’s Melissa Chan reported from Seoul that the family members would not hold a funeral until the rest of the hostages were safely back.
The Taliban has demanded the withdrawal of South Korean troops from Afghanistan and the return of prisoners held by the Afghan authorities.
On Sunday, Ahmadi said the group’s demands remained the same.
He said: “We have the same previous demands; the first is accepting to withdraw the Korean forces from Afghanistan.
“The second demand is still pending as the Afghan government delegation has said that it does not have the authority to release Taliban prisoners.”
Interviewed on Tuesday by Al Jazeera, Kim Jong-yong, South Korea’s ambassador to Qatar, said: “We highly appreciate the efforts being made by the Afghan government and we closely consult them to secure the release of the hostages.”
He said Seoul is not likely to speak directly to the Taliban. “Every day we are briefed by the Afghan government on what is going on between the Taliban and the Afghan government regarding the release of the hostages,” he said.
Kim stressed the South Korean troops in Afghanistan are not on a combat mission but to assist and to rebuild the infrastructure, and also to assist in medical services for innocent Afghans.
He said the Taliban’s demand for exchanging Taliban prisoners with the South Korean hostages “is beyond our capacity to meet”.
In a message to the Taliban, Kim urged them to “stop”, saying that the Koreans being held by the group are innocent people, not warriors, who went to Afghanistan for rendering humanitarian assistance, not for fighting.
He said: “The Taliban’s action of killing the Koreans cannot be justified.”
Source: Al Jazeera, News Agencies